12x12 Queens Puzzle #17
Difficulty: hard. Place 12 queens on this 12x12 board so that no two share a row, column or color region and none touch — including diagonally. This puzzle has exactly one solution, and it has been verified solvable by deduction alone: the complete 25-step reasoning is written out below.
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Step-by-step solution for puzzle #17
What follows is a complete solve of puzzle #17, worked the way a person works it rather than the way a computer does. It runs to 25 deductions — 12 queen placements and 13 elimination steps that narrow the board between them. Each step names the rule that forces it, so nothing below is a guess, and the hardest idea required is the pairing argument on rows.
Techniques this board needs: last square in a region, region shadow, region confined to one line, pairing argument on rows.
Show the full walkthrough (19 steps) — contains the solution
Step 1. Only row 12, column 1 is still open in rose, and since each colour must take a queen, that settles it. That clears row 12, column 1, the rest of the rose region and every square adjacent to it — diagonals included.
Step 2. Indigo is down to 4 candidates in rows 1 and 2, columns 10–12, and they overlap enough to cover 1 square elsewhere. Cross those out without deciding anything about indigo itself.
Step 3. The blue region has 4 squares left, spread across rows 1, 3, and 4, columns 2 and 3. You do not need to know which of them takes the queen: every one of those options attacks the same 1 square, so they can be crossed out now.
Step 4. Wherever mint ends up among its 3 squares, the same squares fall within reach of it — 2 squares in total, impossible regardless of how the colour resolves.
Step 5. Indigo cannot leave row 1 — every one of its open squares (3 open squares) sits there. That row belongs to indigo, so every square on it owned by another colour is dead: 8 squares in all.
The board after step 5 — 1 of 12 queens placed. Step 6. All of the blue region's remaining squares (2 open squares) lie in column 2. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 8 squares come off.
Step 7. Only row 11, column 4 is still open in teal, and since each colour must take a queen, that settles it. Everything else in row 11, in column 4, in teal and in the ring around that square is now dead.
Step 8. All of the slate region's remaining squares (4 open squares) lie in column 3. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 2 squares come off.
Step 9. The khaki region has 3 squares left, spread across rows 8 and 9, columns 6 and 7. You do not need to know which of them takes the queen: every one of those options attacks the same 3 squares, so they can be crossed out now.
Step 10. All of the orange region's remaining squares (2 open squares) lie in column 5. Its queen therefore has to be somewhere in that column, which means no other colour may use it: 6 squares come off.
The board after step 10 — 2 of 12 queens placed. Step 11. Amber is down to 3 candidates in rows 2 and 4, columns 6 and 7, and they overlap enough to cover 3 squares elsewhere. Cross those out without deciding anything about amber itself.
Step 12. The khaki region has 2 squares left, spread across rows 8 and 9, columns 6 and 7. You do not need to know which of them takes the queen: every one of those options attacks the same 2 squares, so they can be crossed out now.
Step 13. Sea green cannot leave row 10 — every one of its open squares (2 open squares) sits there. That row belongs to sea green, so every square on it owned by another colour is dead: 4 squares in all.
Step 14. Here is the pairing argument. The blue and mint regions have no open squares outside rows 3 and 4 — 2 colours confined to 2 rows. Between them they must take one row each, in some order, so every other colour is shut out of all of them: 8 squares come off in one stroke.
The board after step 14 — 2 of 12 queens placed. Step 15. Only row 2, column 6 is still open in amber, and since each colour must take a queen, that settles it. Everything else in row 2, in column 6, in amber and in the ring around that square is now dead.
Step 16. The khaki region is down to one open square, at row 8, column 7. Every colour holds exactly one queen, so that square is forced. Row 8 and column 7 are now spoken for, along with the squares touching that queen.
Step 17. Only row 10, column 8 is still open in sea green, and since each colour must take a queen, that settles it. That clears row 10, column 8, the rest of the sea green region and every square adjacent to it — diagonals included.
Step 18. All of the pale yellow region's remaining squares (2 open squares) lie in row 7. Its queen therefore has to be somewhere on that row, which means no other colour may use it: 5 squares come off.
Step 19. From here the board cascades. Keep alternating the region sweep and the line sweep and 7 queens fall out in order without any new idea being needed: orange has one square left, so its queen takes row 9, column 5; slate has one square left, so its queen takes row 5, column 3; blue has one square left, so its queen takes row 3, column 2; mint has one square left, so its queen takes row 4, column 12; red has one square left, so its queen takes row 6, column 11; indigo has one square left, so its queen takes row 1, column 10; pale yellow has one square left, so its queen takes row 7, column 9. After each one, clear that row, that column, the rest of the colour and the ring of neighbours before looking for the next. The last of them seats the queen on row 7, column 9.
The board after step 19 — 12 of 12 queens placed.
That completes the board: 12 queens seated, one in every row, one in every column and one in every colour, with no two of them touching. Notice that nothing in the sequence above required a guess — each placement followed from an elimination already on the grid, which is what “single solution, solvable by logic” actually means in practice.
About 12x12 Queens puzzle #17
Puzzle #17 is one of the hard-rated boards in the 12x12 set. Twelve colors divide its 144 squares, and you win by placing twelve queens so that each row, each column and each color holds exactly one, with no two queens adjacent in any direction.
There is exactly one way to finish #17, and it has been verified. More importantly, you can reach it without ever gambling: at every stage some square is provably right or provably wrong. Boards differ only in how deep you must dig before that proof appears, and the geometry of these twelve regions is what sets the depth.
How the colors divide this board
From smallest to largest, the regions on puzzle #17 are: rose (1 square), khaki (3 squares), indigo (4 squares), mint (4 squares), teal (8 squares), amber (10 squares), blue (10 squares), orange (13 squares), sea green (17 squares), slate (22 squares), red (23 squares), pale yellow (29 squares). An even split would hand every color 12 squares, so the rose region is running 11 squares under that average while the pale yellow region is the roomiest area on the grid with 29 squares.
Why does the split matter? Because a region's square count has no bearing on how many queens it gets — the answer is always one. So rose, with 1 square, is under far more pressure than pale yellow with 29. A 28-square gap like this one rewards players who start where the choices are fewest.
Look at arrangement as well as area. Rose is the densest region on this grid at 100% of a 1×1 frame; slate is the loosest, occupying only 50% of its 11×4 frame. The loose one reaches into more rows and columns, which is exactly why it usually settles last.
Region by region
Each region's exact extent on this grid is listed below, starting with the most constrained. Knowing which lines a color can and cannot reach is most of the work on a hard board.
Rose occupies 1 square within rows 12–12, columns 1–1. It never leaves row 12, so its queen is locked to that row.
Khaki: 3 squares across rows 8–9, columns 6–7.
Indigo covers 4 squares, spanning 2 rows and 3 columns (rows 1–2, columns 10–12).
Mint occupies 4 squares within rows 2–4, columns 11–12.
Teal: 8 squares across rows 10–12, columns 1–4.
Amber covers 10 squares, spanning 6 rows and 3 columns (rows 1–6, columns 5–7).
Blue occupies 10 squares within rows 1–6, columns 1–3.
Orange: 13 squares across rows 6–11, columns 3–6.
Sea green covers 17 squares, spanning 4 rows and 7 columns (rows 9–12, columns 5–11).
Slate occupies 22 squares within rows 1–11, columns 1–4.
Red: 23 squares across rows 3–12, columns 9–12.
Pale yellow covers 29 squares, spanning 11 rows and 5 columns (rows 1–11, columns 6–10).
Where to start on this board
Open on the tightest color. Here that is rose, confined to 1 square between rows 12 and 12 and columns 1 and 1. Its queen has nowhere else to go, which means those 1 row and 1 column carry more constraint than anywhere else on #17.
Because rose never leaves row 12, its queen must be in that row — and that instantly settles row 12 for everyone else. Sweep along it and X out every square that is not rose. Then look at which colors just lost ground: on a grid this size that one observation usually forces a second region within a move or two.
Work outward to the other flat regions next. Indigo and khaki are no more than two rows tall, so their queens are confined to a narrow band. When two flat regions overlap the same pair of rows, those rows are spoken for and every other color is locked out of both — the single most productive pattern in the game, and it is live on this board.
The tightest lines on puzzle #17
A quick way to find the next move is to count how many different colors touch each line. On this board, rows 7 and 12 are the narrowest, touched by only 4 colors. Column 8 is the tightest column, with 2 colors.
Those lines matter because a row touched by few colors gives its queen away sooner. If a row meets only 4 colors, then one of those regions has to own it, and every other region is competing for the remaining 11 rows. By contrast row 11 meets 6 colors — the most crowded line here, and the one least likely to resolve early. Spend your attention accordingly.
Working through the middle game
Past the opening, treat this as an elimination exercise rather than a placement exercise. Each queen takes out a row, a column and its eight neighbours, and the value of a move is measured by how much it removes. Cross everything out as you go and let the board do the remembering.
Two checks, run alternately, will carry you through the 144 squares of this grid. First: has any of the twelve regions been reduced to a single open square? Second: has any row or column? Either answer forces a queen. Players who stall on 12x12 boards almost always run one of those checks and forget the other.
The trap on a board like this is placing a queen that is merely plausible. Every placement should be traceable to an elimination you can point at. If you cannot name the rule that forced it, you are guessing — and on a single-solution grid a guess costs more to unwind than the deduction would have taken to find.
Why puzzle #17 is rated hard
The hard label comes out of four measurable things about #17: two of its regions are locked to one row or column, its smallest color spans 1 square, its least crowded row meets 4 colors, and its largest and smallest regions differ by 28. Boards that score tight on those measures give up their first queen fast.
Nothing about the rating involves computation or chance. Each grid has a single solution reachable by pure logic; the rating simply measures how far ahead you have to reason. Easy boards resolve a queen every step or two, while hard ones can ask you to carry three unfinished lines of thought before any of them pays off.
Stuck on #17 despite the hard rating? The odds strongly favour a bookkeeping error over a hard chain of logic. Re-check each placed queen for its complete set of eliminations, paying particular attention to the four diagonal squares — those are the ones that get overlooked, and one of them is usually sitting on the answer.
Techniques that work well at 12x12
At 12x12 you are managing 144 squares, and holding the whole board in your head will not work. Split it into quadrants and solve locally. Most useful deductions on a grid this large are regional — a color pinched between two placed queens, or a band of rows that two regions must share. Trust the marks on the board over your memory.
Learn the pairing argument and you will use it on every board, this one included. If two colors can only sit inside the same two rows, between them they consume both rows and every other color is shut out. It generalises to any matching count — three colors across three rows, four across four. On #17, start hunting for it near column 8.
As a sanity check rather than a spoiler: the finished solution to #17 puts 3 queens on the outer border and 9 queens in the interior, 1 of them in an actual corner. If your part-finished grid has queens bunched into one area while whole stretches sit empty, something probably went wrong a few moves back.
How to play Queens
- The board is an N×N grid divided into N colored regions.
- Place exactly one queen (♛) in each row, each column, and each colored region.
- No two queens may touch each other — not horizontally, vertically, or diagonally.
- Tap once to mark a square with an X (where a queen can't go), tap again to place a queen, and once more to clear it.
- There is always exactly one valid solution. Use logic, never guessing, to find it.
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Questions about this puzzle
How hard is 12x12 Queens puzzle #17?
Puzzle #17 is rated hard. Its smallest color region holds 1 square, its tightest row is touched by 4 colors, and two of its regions are confined to a single row or column, which gives you a forced move early.
Does 12x12 puzzle #17 have only one solution?
Yes. Every puzzle in the 12x12 collection, including #17, has been verified to have exactly one valid arrangement of twelve queens, and it can always be reached by logic alone — no guessing or backtracking needed.
Where should I place my first queen on puzzle #17?
Start with the rose region — the most constrained color on this board, with 1 square spanning rows 12–12 and columns 1–1. Narrowing the smallest region first removes the most squares elsewhere on the grid.